Prepare your smoker according to manufacturer's directions. I have an Electric Smoker and I like to use either alder or cherry wood. Set temperature to high and then turn down the temperature.
TIPS: As to the temperature of the smoker, I keep it fairly low (250 degree F). Do not raise the lid of the smoker any more than you absolutely need to (it reduces the temperature inside every time you do).
What constitutes rare and medium-rare cooked meat? To satisfy government home economists, the Beef Council says rare beef means an internal temperature of 140 degrees F. Well, that is OK if you like well done and dry meat. If you like moist, rosy meat (like I do), rare begins at 120 degrees F. and starts to become medium rare at 125 or 130 degrees F. To cook your meat properly, you must purchase and use a good instant-read digital meat thermometer.
Remove from smoker and let it rest at room temperature for 15 to 20 minutes before carving (meat temperature will rise 5 to 10 degrees after it is removed from the oven).
To serve, thinly slice or shave the roast using a shape knife.
Smoked Eye of Round Roast Recipe: https://whatscookingamerica.net/beef/smokedbeefroast.htm